Former Los Angeles police officer Christopher Dorner killed himself Feb. 12 during a siege by police at Big Bear Mountain Lake, Calif. He was suspected of killing four people, including two police officers. / Los Angeles Police Department

by Doug Stanglin and William M. Welch, USA TODAY

by Doug Stanglin and William M. Welch, USA TODAY

LOS ANGELES - Police Chief Charlie Beck said Tuesday it is critical for public trust that his department fully review the firing of Christopher Dorner, the former officer who killed himself last week after a rampage that left four people dead.

"I want to make sure that we address these allegations, which have become so public, in a public way," Beck said.

Dorner wrote in a rambling online posting that he was motivated by anger over his dismissal from the force in 2009.

Beck said the review, announced while a manhunt was underway, will be completed and made public in several months. He said the department often reviews personnel actions, and that it was important for police relations with the community to be open about the review.

"Nothing should be considered closed and done," Beck said. "It's about fairness, and doing the right things for the right reasons," he said.

Dorner's claims of racism and abuse within the department prompted some people to voice support or to sympathize with his complaints. Some labeled him a hero in online postings.

Dozens of protesters held signs in support of Dorner outside police headquarters Saturday, and others have signaled support on a Facebook page titled "I support Christopher Jordan Dorner." The page says it is "not a page about supporting the killing of innocent people. It's supporting fighting back against corrupt cops and bringing to light what they do."

Some have protested the way the manhunt ended: in a fire after officers shot pyrotechnic tear gas into the mountain cabin where Dorner was believed barricaded. Dorner's body was found inside the destroyed cabin, dead of an apparent self-inflicted gunshot wound.

San Bernardino County Sheriff John McMahon has defended the tactics used in the shootout. One of his deputies was killed and another wounded.

"I don't for a minute discount the effect that Dorner's manifesto has had on the reputation of the LAPD," Beck said. "I do not believe that is justified, but it needs to be addressed."

The Los Angeles Police Department has long battled charges of racism and excessive force, especially after the Rodney King case in 1991, when a videotape showed police taking him from his car and beating him. The force has gone through a major restructuring over the past decade in an effort to improve its reputation and relations with residents.

"We are only as good as the public thinks we are," Beck said. "Confidence in law enforcement is our stock in trade."

Beck said it appears that Dorner, who declared war on Los Angeles police and prompted the department to provide security for over 50 families he threatened, stalked some of his potential targets at their homes.

"We believe, based on our investigation, Dorner did his homework," he said.

Dorner was accused of killing Monica Quan, the daughter of a former LAPD captain who represented Dorner at his dismissal hearing, and her fiancé, Keith Lawrence, outside their Irvine apartment. It was also that alleged he shot and killed a Riverside police officer and wounded his partner, and as they were stopped at a light in Corona and wounded two LAPD officers in a separate incident.